# Factor f(x)=2x^{3}+(-3-2i)x^{2}+(-3-i)x+(2+i) into linear factors if 2+i is a zero of the function. Question
Discrete math Factor $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}+{\left(-{3}-{2}{i}\right)}{x}^{{{2}}}+{\left(-{3}-{i}\right)}{x}+{\left({2}+{i}\right)}$$ into linear factors if $$\displaystyle{2}+{i}$$ is a zero of the function. 2021-03-12
Step 1
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Step 2
We Know that Synthetic Division is a method to divide a polynomial by a linear expression.
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}+{\left(-{3}-{2}{i}\right)}{x}^{{{2}}}+{\left(-{3}-{i}\right)}{x}+{\left({2}+{i}\right)}$$
by synthetic division.
we have given 2+i is factor (zero) of function
$$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{2}+{i}&{2}&-{3}-{2}{i}&-{3}-{i}&{2}+{i}\backslash&&{4}+{2}{i}&{2}+{i}&-{2}-{i}\backslash{h}{l}\in{e}-{1}&{2}&{1}&-{1}&{0}\backslash&&-{2}&{1}\backslash{h}{l}\in{e}&{2}&-{1}&{0}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
So, f(x) can be written in its linear form at.
$$\displaystyle{\left({x}-{\left({2}+{i}\right)}{\left({x}+{1}\right)}{\left({2}{x}-{1}\right)}={0}\right.}$$
[Here $$\displaystyle{2}+{i},-{1},{\frac{{{1}}}{{{2}}}}$$ are zero of function]

### Relevant Questions The following problem is solved by using factors and multiples and features the strategies of guessing and checking and making an organized list.
Problem
A factory uses machines to sort cards into piles. On one occasion a machine operator obtained the following curious result.
When a box of cards was sorted into 7 equal groups, there were 6 cards left over, when the box of cards was sorted into 5 equal groups, there were 4 left over, and when it was sorted into 3 equal groups, there were 2 left.
If the machine cannot sort more than 200 cards at a time, how many cards were in the box? (a) find the rational zeros and then the other zeros of the polynomial function $$(x)=x3-4x2+2x+4$$, that is, solve
$$f(x)=0.$$ (type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.)
(b) Factor f(x) into linear factors. (type an exact answer, using radicals as needed. Simplify your answer. Type an expression using x as the variable.) a) Find the rational zeros and then the other zeros of the polynomial function $$\displaystyle{\left({x}\right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4},\ \tet{that is, solve}\ \displaystyle f{{\left({x}\right)}}={0}.$$
b) Factor $$f(x)$$ into linear factors. Find the rational zeros and then other zeros of the polynomial function $$f(x) = x^{3}\ -\ 17x^{2}\ +\ 55x\ +\ 25,$$
that is, solve $$f(x) = 0$$
Factor $$f(x)$$ into linear factors Make fractions out of the following information, reduce, if possible,
1 foot is divided into 12 inches. Make a fraction of the distance from 0 to a-d
0 to a. = ___
0 to b. = ___
0 to c. = ___
0 to d. = ___ Consider the following pseudocode function. function Crunch$$\displaystyle{\left({x}{i}{s}\in{R}\right)}{\quad\text{if}\quad}{x}≥{100}$$ then return x/100 else return x + Crunch(10 · x) Compute Crunch(117). Let $$\displaystyle{F}_{{i}}$$ be in the $$\displaystyle{i}^{{{t}{h}}}$$ Fibonacc number, and let n be ary positive eteger $$\displaystyle\ge{3}$$
Prove that
$$\displaystyle{F}_{{n}}=\frac{1}{{4}}{\left({F}_{{{n}-{2}}}+{F}_{{n}}+{F}_{{{n}+{2}}}\right)}$$ Using cardinatility of sets in discrete mathematics the value of N is real numbers Currently using elements of discrete mathematics by Richard Hammack chapter 18 Let A be a collection of sets such that X in A if and only if $$X \supset N\ \text{and} |X| = n$$ for some n in N. Prove that $$|A| = |N|$$. Let $$\displaystyle{A}_{{{2}}}{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2.2. Let $$\displaystyle{A}_{{{3}}}{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}{A}_{{{n}}}$$ is the set of all multiples of nn except for n,n, for any $$\displaystyle{n}\geq{2}.{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$ Let $$\displaystyle{A}_{{{2}}}$$ be the set of all multiples of 2 except for 2. Let $$\displaystyle{A}_{{{3}}}$$ be the set of all multiples of 3 except for 3. And so on, so that $$\displaystyle{A}_{{{n}}}$$ is the set of all multiples of n except for n, for any $$\displaystyle{n}\geq{2}$$. Describe (in words) the set $$\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots$$.